Given enough time, yes. In my own case, people would estimate about 5000 years . It is time and exposure which makes it possible, plus native people prepared to correct you.

I have proved this possible with German, which I learned as an adult from scratch, until native German speakers thought I was German. At one stage, I was often found out because (quote) my language was too good, and I did not make the correct mistakes. Because any language has regional variations, you can learn a language to a point where a native speaker thinks you are native, but is unable to pin-point the particular dialect (because it is artificial).

This must be possible in Spanish too. German took me about 12 years, working hard . Best of luck .

I've always tried to mimic the way I heard natives speaking Spanish, because I didn't want to sound like a foreigner. That said, native speakers here in the forums have openly admitted that they adore hearing an English accent.

When a native speaker says your Spanish is good, I believe it's a sure sign that they're trying to be nice. This usually means you have an obvious accent.
If they don't comment on your Spanish, you've arrived. Think about how often someone compliments another native speaker on their accent.

If you're able to perfectly mimic a British accent, or any other accent, it's possible to perfectly mimic a Spanish accent.

There are only a few consonants in the Spanish language that are pronounced the same as we say them in American English. We have more vowel sounds in English, and it's pretty difficult for a beginner to narrow them down to just a few, very consistent sounds. You'll only be able to detect these pronunciation differences if they're pointed out to you.

How difficult is it? Hardly anyone who is foreign speaks perfect US accent. Is it possible to learn Spanish accent?

What Rusty says is the same for us non English natives.

The same thing happens to us foreigners. When an English native says that our English is good, usually it is because we have an accent.

One thing for sure, if you practive like Rusty says trying to imitate how Spanish speakers do, and record yourself while reading out loud, revise and retry and so forth, you will get to be fluent and mostlikely your accent will soften. And if you keep doing it you could probably lose your accent altogether.

My own experience matches the comments of both Perikles and Rusty on all points. Through a combination of exposure to many varieties of spoken Spanish, practice, theoretical training and expert coaching I eventually reached the point of having native speakers think I was a native speaker "from somewhere else" for at least a few minutes until I made some error of grammar, vocabulary, or cultural knowledge that marked me as a second-language speaker.

I was able to do a lot on my own by simply paying attention to what I was hearing and mimicking it as best I could.

However, achieving a native-like accent is more involved than pronouncing the individual sounds correctly in context: meaning is also affected by patterns of pitch, stress, intonation and juncture (that is, the ways of pausing between different parts of an utterance); I needed expert coaching to improve them, and I never realized I needed it until I got it as part of a college course on Spanish pronuncation.

...until I made some error of grammar, vocabulary, or cultural knowledge that marked me as a second-language speaker..

Yes, in that order of likely mistake. Even if you achieve the ideal grammar and vocabulary and all else, some obscure reference to, say, a children's story which you've never heard of, can give the game away. Not that it matters much. Body language can play a part too.

In Dublin I was once introduced to a guy and he spoke to me in Spanish. After a while he asked me to guess where he was from. I said Madrid. He said he was Irish. Another time it was a Turkish guy, and I thought he was from Argentina, Uruguay, Paraguay... I've met other people who spoke a good Spanish but it was obvious that they were not native Spanish speakers.

So it's possible.

Some years ago I came across one of my English teachers who was English. After at least 20 years living in Spain, he kept his English accent.

Among speakers of English there is a tendency to become careless with the sounds of Spanish vowels, which are consistently pure. One thing that I (and many others I've heard speak) have to guard against is unconsciously letting the "a" of the final syllable drift into an English-sounding "uh" - a sound that Spanish does not use at all. For example, it's so easy for us in the heat of conversation to slip up and say the word "tomorrow" as mahn-yah-nuh rather than as mahn-yah-nah.

First of all, this is an excellent thread. I work with a lot of guys from Mexico who have had kids in the US. Their kids are raised in the US speaking Spanish at home and english pretty much everywhere else. They don't sound native in either language. I have a neighbor who is Mexican but born here in the US. We talk about Spanish sometimes, but she asked me if she had an accent. I was honest and said yes. She got mad because she wanted to speak like, as she put it, a gringo. LOL! I try my best to pronounce as best I can. I made a choice a long time ago not to be embarassed and that has helped me improve my pronciation. I still have a long way to go, but I wouldn't keep trying if I didn't think it was possible. Again, great thread!